Well everyone will be interested to know how to do this. It is really possible but not for every file. From my experience sound and video are very less compressible. The most common compression format is .rar . The formats .zip and .7zip are also common formats. There is a format known as kgb. It can be compressed with the compressor kgb archiever.
This compressor isnt so common because it takes lots of time for compression and extraction.
Here is the link to download KGB Archiever.
Its great. The only problem with this is that its slow and it may crash in some computers rarely.
You can set a compression level and compress files with this wonderful software. Its amaizing and unbelievable but true. You can google about it for proof.
Its very compressible but has a disadvantage as already mentioned.
The next software for compression is Winrar. This is the best one i have seen. Its comparitively fast and easy to use. I have used several programs which was extracted from this software. I download games etc from sites where it is compressed.
Winrar download link:-
DOWNLOAD WINRARAnathor great compressor is 7Zip.
It is also very common and can compress files highly. It is a newer version of .zip 
7.zip download link is here:-
Also some compressors are winzip and winzix. Winzix is not safe to use according to opinions on the internet.